Academic Skills Advice
Practice Sheet 11: Formulae
Some Useful Formulae:
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𝐴 = 2 × 𝑏𝑎𝑠𝑒 × ℎ𝑒𝑖𝑔ℎ𝑡
Area of triangle:
Circumference of circle: 𝐶 = 𝜋𝑑
(where 𝑑 = diameter)
Area of circle:
𝐴 = 𝜋𝑟 2
(where 𝑟 = radius).
Volume of cylinder:
𝑉 = 𝜋𝑟 2 ℎ
(where 𝑟 = radius, ℎ = height).
Volume of sphere:
𝑉 = 3 𝜋𝑟 3
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(where 𝑟 = radius).
Equations of motion:
𝑣 = 𝑢 + 𝑎𝑡
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𝑠 = 2 (𝑢 + 𝑣)𝑡
1
𝑠 = 𝑢𝑡 + 2 𝑎𝑡 2
𝑣 2 = 𝑢2 + 2𝑎𝑠
(𝑢 = 𝑖𝑛𝑖𝑡𝑖𝑎𝑙 𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦, 𝑣 = 𝑓𝑖𝑛𝑎𝑙 𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦, 𝑠 = 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒, 𝑎 = 𝑎𝑐𝑐𝑒𝑙𝑒𝑟𝑎𝑡𝑖𝑜𝑛, 𝑡 = 𝑡𝑖𝑚𝑒)
(velocity in metres per second, distance in metres, acceleration in metres per second 2 and time in seconds).
1. Use the formulae given above to work out the following:
(Remember 𝜋 ≈ 3.14, and the diameter is double the radius)
a)
Find the circumference of a circle with a diameter of 15cm.
b)
Find the area of a triangle with a base of 8m and a height of 15m.
c)
Find the area of a circle with a diameter of 10cm.
d)
Find the volume of a cylinder with a height of 20m and a radius of 4m.
e)
Find the volume of a sphere with radius 5m.
f)
A car joins a motorway slip road at a velocity of 18𝑚𝑠 −1. After 10 seconds it is
travelling at a velocity of 30𝑚𝑠 −1. How far has the car travelled?
g)
An object starts from rest and accelerates at 15.2𝑚𝑠 −2 until it reaches a velocity of
8𝑚𝑠 −1 . How long did it take?
h)
An object falls from a cliff 40m high. It accelerates at 9.8𝑚𝑠 −2. What is it’s velocity
as it hits the ground below?
i)
A rocket starts from rest and accelerates at 20𝑚𝑠 −2 for 1 minute. How far does it
travel?
© H Jackson 2010 / ACADEMIC SKILLS
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2. Make 𝒙 the subject of the formulae:
1)
4𝑦 = 2𝑥 − 6
2)
7𝑦 = 3𝑥 + 9
3)
𝑄 = 𝑥𝑦𝑧
4)
5)
6)
7)
8)
𝑥𝑦
=8
𝑧
𝑥
𝑚𝑛𝑝
= 5𝑦
15𝑦 =
𝑥
𝑦𝑧
𝑝𝑞
𝑥
= 5+𝑄
𝑥𝑦
𝑚𝑛
−7=𝑍
5
9)
𝑦 = 3 𝑥𝑧
10)
𝑦𝑥 2 𝑧 = 4
3. Rearrange the following:
(𝑏 = base, ℎ = height, 𝑑 = diameter, 𝑟 = radius)
1) The area of a triangle is: 𝐴 =
1
2
𝑏ℎ. Make 𝑏 the subject of the formula.
2) The circumference of a circle is: 𝐶 = 𝜋𝑑. Make 𝑑 the subject of the formula.
3) The area of a circle is: 𝐴 = 𝜋𝑟 2 . Make 𝑟 the subject of the formula.
4) The volume of a cylinder is: 𝑉 = 𝜋𝑟 2 ℎ. Make ℎ the subject of the formula.
5) The volume of a sphere is: V =
© H Jackson 2010 / ACADEMIC SKILLS
4
3
πr 3 . Make r the subject of the formula.
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